Diversity involves difference, but not all difference is diversity. Diversity requires a background of sameness, of a shared nature and shared values. Diversity is difference that still speaks to us, presenting possibilities we might pursue and challenges to which we might rise. Diversity is difference in which we see ourselves, in both our possibilities and our failures.

As biological specimens, humans vary in innumerable ways, small and large, but not all biological difference is the kind of diversity we celebrate. Diversity involves the differences that matter, that reveal our essences and that challenge our self concepts. We are revealed to ourselves by what we recognize as diversity and how we respond to it. Differences can matter to us in two different ways, in ways that celebrate who we are and in ways the challenge it.

We notice some differences because they demonstrate the full potentialities of a form and nature that we share, because they reveal more perfectly what we might be and the beauty of a form in which we participate, that is us. There are countless kinds of laughter, of smiles, of dancing, music, cuisine, and culture. There is a dazzling panoply of different kinds of well-formed human bodies, faces, movements, and expressions. Plato had seen long ago that a fundamental feature of form is its expansiveness, its ability to expand outward into more and more different reflections of itself. In the Timaeus, he remarks of the creator that it would have been regarded jealous, or miserly, had it held back any measure of its overflowing goodness, any possible reflection of its form. Normally we make choices and pursue one possibility, disciplining ourselves to the perfection of one possible flowering of form. But it is the essence of joy and of celebration to overflow boundaries, to seek more and more expressions of ourselves. Differences are beautiful because they are us, our human form, our nature, unconstrained by the boundaries that limit one individual and allowed to flower freely. They celebrate a fullness of human life that no one of us can hold.

Difference can also challenge us. But how it challenges us also reveals who we are, our most fundamental faults, and our most essential value. As far as I can see, differences challenge us in three related ways: (a) they challenge the integrity of the communities in which we develop most fully; (b) they reveal to us our vulnerabilities and fears; and (c) they reveal to us our moral failings. Diversity flowers from the similarity behind our differences and, in so doing, reveals our failures to remain true to our common source.

All of the various forms of our individuality require nurturing and care within a community or family. The purpose of a family or a community, of civilization itself, is to allow for the safety, security, and intimacy in which our individuality can grow and perfect itself most freely. There is in us, therefore, a deeply ingrained, perhaps even biological, tendency to resist the stranger, the different, whatever threatens our communities. There is a fundamental tension involved here: On the one hand we see the necessity of communities that nurture our individuality: we all know what it is like to belong, to be brought inside, to come home. On the other hand, it is the very preciousness of this sanctuary that leads us to exclude those who are different enough to make us feel them a challenge to its integrity. Every community that aims to be diverse must struggle with this tension: We build a community on shared values to foster the growth of the forms of individuality we have chosen, but this makes us exclude those who do not share those values. It is a mark of our status as creatures that we can express the diversity of human nature only in particular ways, as the individuals we choose to be, and that these choices exclude others.

But all this begs the question: Why do we feel difference to be a threat? What differences matter enough to place someone on the outside? What differences define our community? Who is our neighbor? The strong need not fear, and what we know with certainty can admit no doubt. This means that the differences that threaten us reveal our weak spots. Just as we only revel in the diversity that reflects back on our common nature, so we only fear the differences that still present real possibilities for us, that still have some secret hold on us, the reveal some weakness. If someone likes broccoli, while we are allergic to it, we do not feel threatened by their difference. When a difference really gets under our skin, it is always because, in some sense, it really is already within our skin. We feel the pull of that alternative in our common humanity; the spark that lights its fire feeds our flame too. But we feel it pulling us away from the space we have created for our own individuality.

Of course, this reveals the answer to the question “Who is our neighbor?” and the most fundamental way in which difference challenges us. Beneath every difference, in the face that looks out at us, we feel the common spark, the common nature that makes them feel different to us. They are us. Their individuality tries to express the same life as ours. They deserve what we deserve. And yet we feel their difference. They are on the outside, and we fear to let them in. They are our neighbors, yet we cannot bring ourselves to treat them as ourselves. One of Dostoevsky’s major insights was that we do not hate people because of what they are or what they did, but because of what we did to them or what they make us see about ourselves. Seeing difference indicts us of our inability to rise above it. It reminds us of what we would rather not see: that all men are our neighbors and that we cannot bring ourselves to love them as ourselves. Much of the hatred we feel for those different than us involves this deflection of guilt and a demonizing of their differences to escape it.

Now, diversity is not the absence of discrimination. The purpose of education is to make certain kinds of discriminations, between the true and the false, the good and the bad, the beautiful and the ugly. Valuing diversity does not mean that anything goes and that all alternatives are equal. We don’t value a diversity of answers to the question “What does 2 times 3 equal?” Debating our differences about how we make these discriminations is no threat to the real basis of our community. But some human differences are expressions of what we have in common, and the value of our humanity lies in the common spark from which our individuality flows. We may not make the same discriminations another person does, but if we find our differences worth talking about we recognize them as flowing from values we share. We may not love the actions and opinions of every person in their diverse forms, but we are called to love the spark of humanity, in all its conflicts and convolutions, that gives rise to them. They are us; they are our neighbor, and the hospitality of a community that brings them inside can only make it stronger.

There are many kinds of diversity: diversity of styles and preferences, diversity of cultures, diversity of religious belief, diversity of gender and sexual preference, diversity of races and nationalities, diversities too diverse for enumeration; yet all of them reflect our similarities as much as our differences. Diversity celebrates the flowering of the full potential of being human and challenges us to ask of those who, in their flowering, are different from us: Where can I belong, if they do not belong? What do I fear in myself if I fear them? How can I value myself, if I do not value them?

The world is always starting over for us. Out attention shifts from one thing to another; after a good night’s sleep the sun shines again; Spring restores a world of life and growth from the ravages of Winter; a new year presents new possibilities. These recurrences punctuate our lives, breaking them up into units that can appear separate and self-contained; each a chance to start anew. But all of the things that matter in human life take time, extending over boundaries, tying moments together into meaningful wholes: Our attention is focused on the melody of a piece of music, carrying us over the interstices of moments and making a unit of them. A project or a relationship gives unity to our days, giving each meaning by what it contributes to the next. A marriage or a career or a family tie our years together, making them amount to something besides the passage of astronomical units that come and pass like the leaves blowing across the forest floor. Which of these is forgiveness like? Is it a fresh start that distances us from the past, leaving it behind, forgotten, or is it like learning to sing a new song, one that weaves in the past, but in a new way.

We like to think of wiping the slate clean, of making a fresh start for the same reason that doing so is often so difficult. (http://www.anselmphilosophy.com/read/?p=83) We long to be free from our pasts, and it is only our pasts that provide us with reasons for doing anything. We long to be an isolated instant of time with a will all-powerful to make ourselves anew at each moment. But the objects of our will, of our loves and cares, are always outside of us, binding us to objects and their futures. The freedom we have within an instant is always sterile and empty, perishing with the passing of that moment. The fact is, we are always in the middle of things. We never really start over. We are always spinning through time on the momentum of our past loves and hates, on the trajectories of triumphs and failures, careening into the future along the paths we have made for ourselves and that define us. If we started from nothing, began from nowhere, there would be nothing to get us started and nowhere to go. We are lucky that there are no fresh starts, no reset buttons for our lives.

Forgiveness is not forgetting. We sometimes hear that real forgiveness erases our sins, as if they had never occurred, and we often find it difficult to bring ourselves to the purity of such a forgiveness, or to even understand how we could make ourselves forget so completely. But we really don’t want to forget in this way. The love that makes us want to forgive and the love that made us feel harm are one and the same. Can a mother forget the murder of a child without erasing the child and erasing the very impulse to love that fuels forgiveness. Forgiveness is continuing to care about those who have harmed the things we cared about. You don’t forgive by erasing the harms and cares of the past.

To forgive, one must keep before us the harm we wish to overcome with love. When we ask for forgiveness, we do not wish amnesia on the person we have harmed. We want them to see us, in all our faults, and still find a place for us (not an edited version of us) in their hearts. The natural world has a lesson to teach us about forgiveness here. We do not want to erase the persistent essences of things and start the world over anew. We want the sun to shine as it always has, the green of the grass to glow in its light, and the evanescent clouds to shine in its constant light always and forever the same. And God’s forgiveness is nowhere shown to us as clearly in the independent functioning of eternal objects. No matter who I’ve become or what I’ve done, these things will remain the same for me, if I only retain the courage to accept and respond to them. No matter how inexplicable it may be that the sun shines still for the likes of me, the world, at each instant, welcomes me into its future just as it always has, for saint and sinner alike.

In the same way, unconditional love, does not ignore our faults and transgressions, but refuses to cut us off, dwelling forever in the past with them. In its essence, love, too, exists in time, always seeing more in our futures than our pasts can contain. Despite our transgressions, the infinite value of our individuality still functions independently, calling us to a future that transcends our sins. To love someone even in their sins is not to love their sins, but to see that person as not contained in the past, to see them always with a trajectory towards the future, living in hope that the good in them will function always and everywhere the same and fulfill itself in their future. Forgiveness sees clearly and feels clearly the harms of the past, but draws the transgressor back into our future in hopes that they will be more than their past. It does not start over with a clean slate, but writes a new story and sings a new song, in which our sins are not the end of the story. Forgiveness is the triumph of future over past.

“Did you say the stars were worlds, Tess?”
“Yes.”
“All like ours?”
“I don’t know, but I think so. They sometimes seem to be like the apples on our stubbard-tree. Most of them splendid and sound – a few blighted.”
“Which do we live on – a splendid one or a blighted one?”
“A blighted one.”
— Thomas Hardy (Tess of the D’Urbervilles)

Do you feel lucky to be here? How lucky do you have to be in order to require a special explanation of that luck? Some philosophers and scientists have argued that the very improbability of our being here, of the universe being constructed so as to allow the conditions for intelligent life, requires a special explanation, a God, or intelligent designer, behind the original conditions of the universe. Part of the impetus for such arguments comes from an awareness of how the development of the universe depends upon certain variables that are not derived from anything else, but which are traced back to certain original conditions within a primordial singularity or big bang. Supposedly, when one looks at the number of such variables and the possible values they could have taken, the possibility of a universe arising in which one gets things such as stars and planets, or any kind of matter of the sort we know, is so small as to defy understanding. Roger Penrose has calculated[1] the probability of a universe that might contain the preconditions for life as 1 in 10 raised to the 10123 power. (That is 10 followed by more zeroes than there are particles in the universe.) According to this, all of us have pulled out the one lucky ticket out of gazillion-zillion-zillion losers in the cosmic lottery. Do you feel that lucky?

The philosopher, Daniel Dennett, has suggested[2] that this type of line of reasoning makes a simple logical mistake, jumping from a very obvious restriction on the type of things we can expect to observe to a very dubious conclusion about the origin of those conditions. Physicists sometimes call the starting point and ending points of this jump the Weak Anthropic Principle and the Strong Anthropic Principle, respectively. The Weak Anthropic Principle is sometimes stated as a recognition of the observation biases we find due to the limited range of possibilities we can observe. Just as we can only expect to see, with our naked eye, the small range of electro-magnetic phenomena that are visible to us; so we can only expect to observe the small range of possible configurations of the universe that are compatible with our existence. If we exist, then the conditions necessary for our existence must obtain. Stated this way, this seems just about as obvious as anything could be. If I am here, then none of the things that could have prevented it have happened: I haven’t been shot, run over by a car, had a heart attack, or any of the other things that could have prevented me from being here. I am not particularly lucky in having avoided these things. That I have avoided them doesn’t require any special explanation. Of course, if I am here, then none of these things happened, but there is no special reason that they didn’t; they might have. The Strong Anthropic Principle suggests that these original conditions, that the universe is capable of supporting intelligent life, are somehow necessary, and it is this necessity that requires special explanation. If, as I was walking over to my office, a car attempted to run over me and mysteriously swerved at the last moment; if no matter how determined the attempts to take my life, they were somehow thwarted (as in a Pink Panther film), then I would be lucky in a way that requires explanation. The question is whether the origin of the universe is like this kind of case. Dennett merely points out that this does not at all follow from the weak version of the principle.

William Lane Craig has suggested[3] that the origin of the universe is, indeed, more like this kind of case, comparing it to a firing squad that misses mysteriously. If 25 marksmen with perfectly functioning rifles all train their guns on a man at 50 paces, it is vastly improbable that they all should miss. If one of them typically misses such a shot only 1 in a 100 times, the probability of them all missing is 1 in 10025 or 1050. One would not expect a miss if they fired once a second from the beginning of the universe 1017 seconds ago until now. If such a thing happened, we would most certainly require a special explanation, such as that they all disobeyed orders and missed on purpose. And, of course, this improbability is small compared to the super-super-astronomical improbability of the original conditions of the current universe according to calculations such as Penrose’s.

The real question is whether the assumptions that allows us to draw inferences in cases such as these apply to the original conditions of the universe. When we calculate probabilities we draw inferences from the formal structure of a situation based upon certain assumptions, chief of which are (1) The choices between the different possibilities are completely random; and (2) We are considering the probability of one unique instance, specifiable in advance. We cannot know to any degree of certainty that either of these conditions obtain in the case of the origins of the universe. Let us consider the second assumption first. When a meteor makes it through the atmosphere, it is certain to hit somewhere; though of all the innumerable places it could hit, it is improbable that it will hit me. After the fact, if we find the unlucky person that it hits, even though they are only one of the millions of people it could have hit, the fact that it hit them requires no special explanation; it had to hit someone after all. When we reach into a hopper full of 1000 white balls, each with a number, and pull out number 367, the odds of pulling that number out were 1 in 1000. Yet surely, I would be silly to thank my lucky stars for pulling off a 1 in 1000 shot. Each of the other indistinguishable possibilities was also a 1 in a 1000 shot, and there were 1000 of them, hence it was certain that I would get some number or other. If, on the other hand, there were one special number, specified in advance, and I was able to choose that and win the lottery, this would seem to require some special explanation. Again, this assumes that this instance is unique. If I repeated my attempt 1000 times, it would be even money that I would get the lucky number at least once. Imagine that in 999 other rooms, unknown to me, there are 999 other identical hoppers with other people choosing 1 of the 1000 balls. I may feel lucky, but the odds were that one of us would pick the lucky ball. Dennett, along with many other thinkers, has pointed out that if this universe is not unique, if innumerable other multiverses are playing the cosmic lottery, odds are that someone had to win, so it is not surprising that we find that we did. But, in this case, the very nature of the singularity from which the universe arose seems to prevent us from knowing whether this roll of the dice is unique or not.

Likewise, we have no way of knowing if the choices between the various different values of the constants in Penrose’s calculation are equally likely and taken at random. It turns out that 81 times 114,839 is equal to 9301959, the exact date of my birth. Is this a lucky stroke? Are the gods of mathematics preordaining the universe to my amusement? After all, there are 10 million other 7 digit numbers that could be the answer to that problem. But just as 2 times 2 couldn’t be anything but 4, so we may think there is nothing else that could be the answer to this particular multiplication problem. Are the different possible values of the cosmic constants equally likely? Could there be something that constrains them or renders them necessary, of which we cannot be aware? Again the very fact that the causal chains, which provide us knowledge, can reach back no farther than the Big Bang, renders it impossible, in principle, to answer these questions. In such cases, the conditions that allow us to draw inferences from probabilities, simply cannot be known to apply.

I am not enthusiastic about the Anthropic Principle as evidence for God’s existence, but I do like to think about it, since it reveals interesting things about how we think about chance and Providence. If this universe is the result of an intelligent agency, the most interesting thing about it will not be its existence, no matter how unlikely: Note that in the above cases there was nothing interesting, requiring special explanation, about me being the one being hit by the meteor or being the one who wins the ball lottery if 1000 others are playing as well. There was nothing about me, specifiable in advance, that made me unique. Yet to me it makes all the difference.[4] There have been about 106 billion human lives in this unlikely universe, of which about 7 billion are going on now, about 5.8 percent.[5] Of these, 80% live in abject poverty[6], with an even larger proportion of those who lived in the past, leading even more miserable lives, subject to the worst kinds of pains, fears, and misfortunes. So only approximately 5 of 100[7] of the humans ever to have lived has ever been as fortunate as you. As we sit here at our computers, full of belly, warm of foot, healthy and well contented, we can see that there is nothing about us that could have been specified in advance that renders us more deserving than any of the other human souls to inhabit this unlikely universe, sole supporter of intelligent life, the winner of the cosmic lottery. Yet here we are. Do you feel lucky?

At one time most of my friends could hear the bell, but as years passed it fell silent for all of them. Even Sarah found one Christmas that she could no longer hear its sweet sound. Though I’ve grown old the bell still rings for me, as it does for all who truly believe. (Polar Express)

At the bottom of the heart of every human being, from earliest infancy until the tomb, there is something that goes on indomitably expecting, in the teeth of all experience of crimes committed, suffered, and witnessed, that good and not evil will be done to him. It is this above all that is sacred. (Simone Weil)

Imagine explaining Christmas to an alien. Surely it would be strange to attempt to explain Santa Claus to someone completely unacquainted with the custom. Even once one got past the difficulty of explaining the religious significance of the holiday that celebrates God’ s redemption of humanity by his being born as a child and the tradition of giving gifts as an imitation of this ultimate gift, there would still remain even more and greater strangeness. We give our children gifts but pretend that they are not from us, but from this imaginary kind-hearted Santa Claus, who watches the naughty and the nice and grants the wishes of all the world’s children. We smile with tenderness at the innocence of our children as they absorb this belief and allow it to tinge the appearance of presents under a tree on Christmas Eve with a magical, mysterious glow. And we grieve, in a way, when the illusion is lost to the inevitable advance of our children’s knowledge of the practicalities that govern our world and the laws that govern the human heart. Why? Why do we do this, and why do we feel a great loss when we come to see it all as humbug?

It is surely no virtue to lie, nor is it worthwhile fostering an ability to be deceived, even about things that we might wish were so. The value of believing cannot lie in a willed ignorance of what is right before our eyes, but in a hope for a deeper truth that lies beneath the surface of things. All magic lies in there being more to things than meets the eye, in there being hidden virtues and powers hidden within the heart of things that cannot be revealed in their appearances without special probing and prompting.

It may seem that there are no two things more dissimilar than scientific knowledge and belief in Santa Claus, but I believe that there is a deep connection between them that reveals the value of belief of this sort. The scientist learns to probe beneath the surface of things, to believe that within the flux and chaos of normal experience there lie hidden laws of nature that exhibit themselves only to the initiated under controlled conditions. The natures of things, as Plato saw, exist eternally and purely, and can only be revealed in things as they come to fulfill them in time, in the absence of interference and impurity. A scientist must see in the complex morass of empirical data, a hidden structure. He must have confidence that at the heart of chaos, lies law; that the random ramblings of the most unruly particle is in the grips of a form, a law that will be revealed by its behavior only over time under pure enough experimental conditions. The scientists who sit and wait in the super-conducting super collider for the particle predicted by the exquisitely beautiful mathematics of their physical theory are waiting for Santa Claus.

Just as the scientists can work only in the hope the mathematical order to which his mind responds is reflected in the order of nature, so in the innocent heart of a child there lie the urgings of beneficence and love. Like the secret forms of the natural world, hidden in its complexity, these seeds lie amongst our passions and the practical requirements of our world, which interfere with their expression. Just as the scientist believes that reality, in the grips of a form, in the fullness of time, will exhibit the actions that mathematical laws prescribes, so the innocent, pure soul in the grips of these most scared urgings of the heart (as Simone Weil calls them) hopes for good rather than evil, that kindness will be returned, that their letters to Santa will be answered.

According to Weil, we grieve the loss of belief, because this ability to feel ourselves in the grip of eternal forms, forms that express themselves in this world only in pure circumstances in the fullness of time, whether these forms be forms of natural law or forms of life and love; this ability is the most sacred part of human nature. I don’t think this has much to do with the gullibility of believing in pleasant things, whether they be religious dogmas or cute fairy tales. There is a rationality to the belief of the scientist and the child. The things that matter, in both science and life, are more than what meets the eyes; they are things whose expression requires the fullness of time and purity of condition. We are sometimes mistaken in our ascription of form to the natural world, but only the man who believes, beyond all hope, in the face of the fear of error, that there is an order at the heart of motion of the planets, will discover it, as Kepler did. Often kindness is repaid with pain, and no unknown stranger provides hidden acts of kindness to delight us, but only those who keep alive the secret urgings of their heart to see the good, and expect it in all men in the fullness of time, will have the courage to build the types of conditions, as rare and difficult as a super-conducting super collider, in which these urgings can come to fruition. Only those that continue to hear the hidden ringing of the bell, inside the hollow metal shell, will discover one day as they sit back exhausted in the silent gleaming, after arranging presents quietly under a magically glistening tree, that there is indeed a Santa Claus, and that it is them.

And you shalllove the LORD your God with all your heart, with all your soul, with all your mind, and with all your strength.’ This is the first commandment. And the second, like it, is this: ‘You shall love your neighbor as yourself.’ There is no other commandment greater than these. —Mark 12:30-31

If a thing loves it is infinite.— William Blake

Love goes beyond all bounds. Two things loved with all one’s heart must be equal. If you love others exactly as yourself, there will be no way of choosing between them, or between them and you.

It is often thought that a teleological ethical system, one that derives its theory of moral actions from a theory of the good, cannot account for the intrinsic value and dignity of human life. Utilitarianism, for example, is often criticized because it seems to make the overall happiness of a group justify sacrificing the values of the individual. The needs of the many seem to outweigh the needs of the few. But this only applies if the goods being balanced are finite. No number of finite goods can balance an infinite good.

While we shouldn’t pretend that using mathematical language gives our ethical intuitions more precision and certainty than they have, I do believe that there is something to be learned from looking at the way in which mathematical concepts of infinity work. Just as it may seem strange that no collection of finite numbers will add up to an infinity, so it may seem strange that no number of grasshopper lives will add up to a human life. Infinite quantities also confound our intuitions when we add finite numbers to them (no matter how much you add to infinity, you still just have infinity) and when we consider adding infinity to infinity (no matter how many infinities you add to infinity, you still just have infinity).1 So it may seem strange that no matter how much finite value we add to a human life, it is still not worth more than another; or that no matter how many human lives we take together they still do not justify the willful destruction of one human life. Much of what is strange about the value of human life is part and parcel of the strangeness of infinity.

What makes the value of a human life infinite? This is a bit harder to say, and while here I am mainly interested in drawing out the consequences of this proposition rather than defending it,I do think that there are two useful things one can say: (1) A will that loves goes beyond all bounds. When you care about something, all other things being equal, you care about it always and everywhere. To feel joy is to desire to feel it always. To grieve at the loss of a child, is to grieve for all the lost children, wherever they may be. Though our will finds itself impotent to create the realities of the things it values, the reach of its commitments is not bounded by space or time. (2) The will can order its values into systems of commitments that transcend the individual values from which they arise, in fact, the will may be defined by such abilities. Our love for a person is more than just the sum of our enjoyments of the moments we’ve spent with them. Just as a melody is more than just the sum of its notes, the will synthesizes our values into new unities that transform the individual values as they come to exist within the new whole. One of the great discoveries of Gregor Cantor was that there are levels of infinity even greater than the infinity of the natural numbers. The number of real numbers on the number line (including both the rational and the irrational numbers) is a level of infinity (aleph one) that cannot be reached by adding any number of infinities. This new level of infinity arises from taking the power set, the set of all subsets, of the natural numbers. In an infinite world of values, the will has an unbounded ability to synthesize new values, integrating novel combinations of commitments in new ways. We can love things in more ways than there are things to love.

What would an ethics of infinite love look like? It will not generate a rational procedure to determine with certainty what you should do or to be sure that you have done what is required. There will be no unique way of balancing infinite values against each other, nor any way of satisfying the infinite demands of our values. It will not spare you the anguish of moral choice nor the urgings of conscience.

With no recipe for action, it will be the character of our love that will matter rather than the characteristics of our action. The two commandments quoted above are the best summary of such an ethics, and they might be summarized more succinctly as “Love the good without bounds” Or as C.S. Lewis puts it, “act in time, as beings destined for eternity.”2

An ethics of infinite love would also mean that we can never meet the infinite obligations that our love places on us. Once you start caring about the hunger of children, you will find that there are more of them than you can even think of, let alone feed. Once you allow yourself to feel the infinite value of each set of eyes that look at you, you will feel yourself to be, in Dostoevsky’s words “responsible to all, for all.”

This is not meant to be an invitation to despair; we were given wills that, while impotent in their power, were infinite in their reach. It is the depth of our care that leads to its infinity; we do not cease caring about things simply because we cannot achieve them: We feel our loves, for the things we care most deeply about, as a thirst for which there is no quenching3, from a cupful of goods that knows no bottom. The ethics of infinity reveals us to be creatures always in need of redemption, but also as beings capable of living in its hope, in the draft of a current that ends beyond the horizon.

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1This is more precisely stated by saying that all ordinal infinities (those arrived at by adding one more) all have the same cardinal number (aleph null); all are still equinumerous with the natural numbers or integers, or are still countable infinities.

The members of the Philosophy Department were asked which book they thought would be important to teach to students in an introductory philosophy course. Their answers are below. You can listen to them all at once or you can click on the name of the individual professor below to listen to each professor’s answer.